A clamping device of this type is known from DE 10 2004 026 438 A1. Within the machine spindle of this device, a drawbar is disposed, said drawbar being able to move between a clamping position and a release position and being actuated by a clamping spring into the direction of the clamping position. On its front end, the drawbar has a clamping cone with a plurality of clamping elements which rest against the outer surface of said clamping cone and which, via the axial movement of the clamping cone by means of the drawbar, can be moved back and forth between a clamping position in which a tool or a tool holder is retained in the machine spindle and a release position in which the tool or the tool holder is released. In addition, one or more sensors for monitoring the clamping forces or clamping statuses are also disposed within the machine spindle. However, since the components of the clamping device that are disposed in the machine spindle do not only rotate but also execute a relatively large lifting movement, the transmission of the measured data acquired by the sensors between the moving and stationary components of the clumping device presents a problem.